There is nothing illegal (not saying it's not tacky or otherwise) for someone to stand outside someones house and photograph the people outside.
State the case law that says you cannot be photographed while in public view
I still believe it may be improper to photograph a private person and publish the photos to third parties without their consent, in connection with an implication that a law is being broken. As to case law on publishing an private individual's information or likeness;
Article I Section 23 of the Florida Constitution,
Rivers v. Dillards Dept. Store, Inc., 698 So.2d 1328 (Fla.App. 1 Dist., 1997)
Agency for Health Care Admin. v. Assoc. Indus. Of Florida, Inc., 678 So.2d 1239, 1252 (Fla. 1996)
Cason v. Baskin, 155 Fla. 198, 20 So.2d 243 (Fla. 1945)
and multiple others concerning publishing the private information and/or likeness of a private individual without permission.
But in this case, the "evidence gatherers" aren't acting on their own behalf, or for any commercial purpose. Rather, they're acting in order to gather probable cause for COJ's property enforcement operations, and because this is the scope of their actions, they're going to be held to the same standard as COJ would be under the same circumstances.
And to answer that question;
State v. Parker, 399 So.2d 24 (Fla.App., 1981)
State v. Butler, 1 So.3d 242 (Fla.App. 1 Dist., 2008)
State action is present, for Fourth Amendment purposes, when (1) a private party acts as an instrument or agent of the state in effecting a search and seizure, and the government knows of and acquiesces to the conduct, and (2) the search is conducted solely in pursuit of a governmental interest, rather than the private actor's self-interest. U.S.C.A. Const.Amend. 4
So where does that leave us? The self-described "probable cause gatherers" will probably be held to the same standard as the governmental entity making use of the information. So then you have to ask yourself whether anything they find can be used to support a finding that a property is a rooming house. That depends on the extent to which someone's privacy rights are invaded. This will be a case-by-case basis, and if the photographs are violative then they can't be used.
However, there appears to be only one case that is directly on point in Florida for the situation we're discussing, namely photos being taken by neighbors and then turned into code enforcement and the owners later alleging this violated their privacy rights;
Town of Sewall's Point v. Rhodes, 852 So.2d 949 (Fla.App. 4 Dist., 2003)
This case involved neighbors taking photographs of private property and turning them into the City for enforcement purposes, and then the landowners later alleging this violated their right to privacy. The case didn't go well for the owners. Even when the photographs were labeled by the neighbors "The Hillbilly Hellhole", the court still found this was not defamatory and did not violate any of the landowner's privacy rights. So that does seem absolutely dispositive that the property owners' rights aren't violated by this type of photography.
But the rights of other people on that property may be another story. There just isn't much law on this exact point, except for the above case, which admittedly seems to find no problem with it, although again I'm stumped because that only related to the owner's rights and not to random people in the photograph.
Honestly, after researching it, I've got no clue. At first, I'm inclined to say
Dillards would dictate you can't photograph people without consent and wrongfully publish the photographs implying they're breaking a law, but then the purpose of these photographs isn't to imply that the people being photographed (the rooming house residents) are breaking any law. Their purpose is to imply that the landowner is breaking a law, and the landowner doesn't appear to be protected, according to the appeals court's review of
Sewall's Point. But again, that was property not people. So honestly, who knows?